一类多项式全局优化的差分算法

A Difference Algorithm to Find Global Minimizers of a Polynomial

摘要:

引入一类n元多项式的倒向微分流以求解全局优化问题.沿着倒向微分流，建立一个差分 牛顿混合算法，并证明了由算法所得迭代点的绝对误差受到差分步长的一致界囿.应用所建立的算法，给出了一个数值计算的例子.

关键词:多项式全局优化; 倒向微分方程; 差分牛顿混合算法

Abstract:

This paper presents a differential flow concerning the global optimization with polynomials. Along the flow which leads to a global minimizer there is posed a mixed difference algorithm with Newton method. An error analysis of the algorithm is given with a numerical example to demonstrate the mixed difference method.

Key words:global optimization with polynomial; backward differential flow; mixed difference algorithm with Newton method